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1989 (EN)
Hereditary order convexity in L(X, Y) (EN)

Hadjisavvas, N (EN)
Kravvaritis, D (EN)
Pantelidis, G (EN)
Polyrakis, I (EN)

N/A (EN)

Let X be a topological vector space, Y an ordered topological vector space and L(X, Y) the space of all linear and continuous mappings from X into Y. The hereditary order-convex cover [K]h of a subset K of L(X, Y) is defined by [K]h ={A∈L(X, Y):Ax∈[Kx] for all x∈X}, where [Kx] is the order-convex of Kx. In this paper we study the hereditary order-convex cover of a subset of L(X, Y). We show how this cover can be constructed in specific cases and investigate its structural and topological properties. Our results extend to the space L(X, Y) some of the known properties of the convex hull of subsets of X*. © 1989 Springer. (EN)


Εθνικό Μετσόβιο Πολυτεχνείο (EL)
National Technical University of Athens (EN)

Rendiconti del Circolo Matematico di Palermo (EN)


Springer-Verlag (EN)

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